If you look in our Homeschool vs Public school area, you'll find links to statistics (some of which are on socialization), as well as plenty of discussion threads on the topic. It all boils down to this, though - public school does not have good socialization (or if it does, you're probably not spending enough time studying), and extracurriculars are where the good socialization is found. Since homeschoolers can finish their regular schoolwork in half the time of public schoolers, that leaves them a lot more time for extracurriculars, therefore their socialization should be better, not worse. This assumes, of course, that they make the effort to go out and do things with their extra time.

Socialization is really a lousy argument against homeschooling. It's easy to get plenty of good socialization, assuming you're motivated enough to make the effort, and there are plenty of public schoolers who sit in school for eight hours a day, surrounded by dozens or hundreds of other kids, and still have no friends. And even if you do have plenty of friends in school, all you're learning is how to interact with other kids, since the adult-child ratio is so low, and that won't help you much when it comes to college or the business world. Extracurriculars at least have more adults and (usually) more mature kids, so they're better at building the socialization skills you're actually going to need.

If you have to write a persuasive letter in order to homeschool, include all of the ways that your child(ren) will be around and interacting with other children. write about the people that they will see, family, friends, activities, groups, clubs, interacting with people that you see while you do your everyday activities, the store, the post office, walks around the area. Think of all the ways that you will see people and that is the best socialization that your child can get, multi generational, (all ages). That is real life, talking to people of ALL ages.